Best answer to the question is Vattel’s Law of Nations which was the source of the phrase, Natural Born Citizen.It requires the child to be born of TWO CITIZEN parents and born on US Soil.
The question being asked, IMO, is how the clause found its way into the draft and what Washington and the ratifiers understood and intended with the language. (In this regard it is helpful to recall the Constitution is a contract, not legislation.)
Washington, of course, intended what Jay suggested for the CinC. Jay's suggestion was clear: an ordinary citizen, as thought of at the time, was not sufficient.
What sort of higher citizenship was required? The highest class of citizenship remaining at the time was that which precluded allegiance not only by birthright but also by parentage to any foreign nation.
Whether the ratifiers were versed on Vattel or not, they well understood by virtue of their most recent bloody war with England, the boundaries and necessity of allegiance.